UPSC NDA Math Model Paper 7

Let A: Heart is drawn from a pack of cards.
Let B: An ace is drawn from a pack of cards
As we know that, probability of an event is given by: P(E)=

n(E)

n(S)

So, probability of winning the bet is given P(A or B ) i.e P(A∪B)
⇒P(A)=13∕52,P(B)=4∕52 and P(A∩B)=1∕52
As we know that, P(A∪B)=P(A)+P(B)−P(A ∩B)
⇒P(A or B)=P(A∪B)=

13

52

+

4

52

−

1

52

=

4

13

∴ Probability of losing the bet =1−

4

13

=

9

13

∴ Odds against winning the bet is

9

13

:

4

13

=

9

4

Hence, option A is the correct answer.